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TRANSCRIPT
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13th
World Conference on Earthquake EngineeringVancouver, B.C., Canada
August 1-6, 2004Paper No. 3177
NONLINEAR SEISMIC RESPONSE ANALYSIS OF
PILE-SOIL-STRUCTURE INTERACTION SYSTEM
WANG Feng-Xia1
HE Zheng2
OU Jin-Ping3
SUMMARY
In this paper, by using ANSYS
software, a modified lumped-mass simplified nonlinear pile-soil-structure
interaction (PSSI) model is established for shear-type RC frame structure under moderate and large
earthquakes with rocking effect, dynamic nonlinearity of interaction between pile and soil, the contact
state between pile and soil, raft and soil. Seismic response of a 4-storey building supported on piles is
analyzed with respect to linear and nonlinear pile-soil systems using this model, and is compared with the
behavior of buildings with rigid base under moderate and large earthquakes. A simplified model is
presented to apply for the engineering applications.
INTRODUCTION
Under moderate and large earthquakes, the pile-soil-structure interaction (PSSI) system presents the
evident nonlinear feature. In this case, it is necessary to take account of the nonlinearities induced in thesoil of the free field by seismic waves and of the additional nonlinear effects created by the structural
vibrations.
Approximate theories have to be used because the rigorous approach to the nonlinearity of pile-soil-
structure system is difficult. Lumped-mass model proposed by Penzien[1]
is a popular approximate
method to solve the soil-structure interaction account for its convenient application to engineering
practices.
Many FEAsoftwares with the development of the computer technologies have been developed to the highquality engineering tools, which can be used to design, and analysis. Such as ANSYS
, that can provide a
common platform for fast, efficient analysis in a lot of important areas. Thus, the soil and structure
interaction should utilize this effective tool, too.In this paper, a modified lumped-mass simplified model is established for shear-type RC frame structure
under moderate and large earthquakes based on the Penzien, by using ANSYS software. Using this
1PH.D. student, School of Civil Engineering, Harbin Institute of Technology, Harbin, China,
email:[email protected]
Associate Professor, School of Civil Engineering, Harbin Institute of Technology, Harbin, China,
email:[email protected]
Professor, School of Civil Engineering, Harbin Institute of Technology, Harbin, China,
email:[email protected]
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model, a 4-storey building supported on piles is analyzed with respect to linear and nonlinear pile-soil
systems, and is compared with the behavior of buildings with rigid base under moderate and large
earthquakes. Furthermore, the parametric influence of the system is studied. It suggests that the
contact state of pile and soil changes from contact and slippage to separationunder seismic load,
and the behavior of the building supported on a pile foundation is different from a rigid base.
Moreover, the nonlinear seismic response of a building including the PSSI effect is differentfrom the linear response. The model built by ANSYS
is easy to apply for the engineering
applications.
COMPUTATION MODEL AND PARAMETER DETERMINATION
Computation model
The hypotheses of the model are as follows: super-structure is simplified to shear-type RC frame structure,
the pile group is assembled into single pile with the abilities of bending and shearing, and super-structure,
piles and soil around piles present linear behavior, lateral soil resistance is nonlinear, furthermore, the
contact nonlinear effect between piles and soil is taken into account.
governing equationsIn present, Penzien model is one of soil-pile interaction system models widely used in practice, because it
is simple and conceptual definitude. But this model does not consider the dynamic effect of soil around
pile directly, and motion input is multi-points input format with different soil layer different motion input.
The modified model takes account of several factors based on the Penzien model. First, free-field ground
(soil around pile) simulated by PLANE element is considered into the model directly, and the viscous
damping elements (COMBIN14) are set at the boundary of the free-field ground to simulate the radiation
damping, thus motion input in this model can be input from the rock with the one motion input datum, so
this model simplifies the computation process and presents dynamic interaction between the piles and soil
factually. Second, pile is simulated by BEAM element and two vertical springs (CONTAC12) at the end
of raft present the rocking effect. Third, using p-y curve simulates the nonlinear resistance between pile
and soil, then the contact state of the interface between pile and soil is presented under dynamic load with
contact elements,. The PSSI model is shown in Figure 1.
The governing equations referred in [2] and [3] can be given as follows:
Super-structure: (1)gx1MxKxCh)x(M rrrrrrr &&&
&&&& =+++
Figure 1. Simplified model of a pile-soil-structure
system
Super-structure
Free-field
Raft
Pile
Super-structure
Radiation
damping Soil Vertical
spring
with
Bedrock
gx&& gx&&
Contact and nonlinear
spring
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Pile foundation: (2)
Raft: (3)
(4)
Soil around pile: (5)
In which the subscript r, p and s stand for superstructure, pile and soil, respectively; M, C and K arethe
mass, damping and stiffness matrices, respectively; X, h and F are the displacement vector, floor height
vector of super-structure and lateral soil resistance vector, respectively; m0,J0,, h and x0 are the mass, the
moment of inertia, the rotation angle, the thickness and the relative displacement of the raft, respectively;
f0 andMare the horizontal resistance and resistant moment of raft given by soil; hiis the distance from the
floor to the raft; gx&& is the acceleration of motion input.
Parameter determination
Super-structure parameter
Super-structure is simplified to shear-type structure, whose parameters determined according to the
reference [4].
The horizontal resistance and resistant moment of raft
The horizontal resistance of raft is computed by the equation (6)
(6)
where k0 is the lateral soil resistant stiffness coefficient of the raft, which can be developed as
(7)
where bf0 is the computational width of the side of the raft, which is determined by the reference [5]; c0 is
the damping factor; and m* is the resistance factor of the soil to raft, which is referred to the reference [6].
The resistant moment of raft can be computed with equation (8)
(8)
wherecap
K is the total rotational stiffness, can be determined by the reference [7]
(9)
where KRR is the rocking stiffness of a pile group, KRR=ri. iF , in which ri is distance between the
center of rotation and the pile heads center, and Fi is the axial force at the pile heads, K is the
rotational stiffness at the head of pile, when the heads of a pile group are the raft, the equation (9) can bemodified as equation (10).
(10)
where K is the rotational stiffness of the raft,)1(3
8 30
=
GrK , 4 00
4
Ir = ,I0 is the moment of inertia of
the raft, G is the shear module of soil, v is the Poisson s' ratio of soil.In this model, the rocking effect is simulated by the two vertical springs considering the contact influence
between the raft and soil at the side of raft; the vertical spring stiffness can be developed as
0)2
()( 0001
=++++++=
fh
xxmxhxm ggin
iriri
&&&&&&&&&&&&
2
2*
00
hmbk f=
cap
KM=
+= KKK RRcap
KKK RRcap
+=
gx&&&&& 1MFxKxCxM sssssss =++
)()( 00000 ss xxcxxkf && +=
gx&&&&& 1MFxKxCxM pPppPPP =+++
02
)2
()( 001
0 =+++++++ =
Mhh
xxmxhxhmJ ggirin
iiri
&&&&&&&&&&&&&&
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2
R
KK
cap
= (11)
where R is the distance from the center of the raft to the side of the raft.
Lateral soil resistant stiffness coefficient determination
There are many methods to determine the lateral soil resistant stiffness coefficient, in which the mostcommonly used method to solve the nonlinear lateral soil resistance is p-y relation curve. Lateral loads on
piles are resisted by the surrounding soil whose behavior is characterized by lateral soil resistance per unit
length of pile, p, as a function of lateral displacement, y. The p-y relation is generally developed on the
basis of a semi-empirical curve, which reflects nonlinear resistance of the local soil surrounding the pile at
specified depth. The two most commonly used p-y models are those proposed by Matlock (1970) for soft
clay and by Reese et al. (1974) for sand. In this paper, the p-y model proposed by Reese for sand is used to
analysis the 4-storey building supported on piles. The parameter determination of p-y relation curve can be
referred to the reference [6].
PSSI system damping
In the pile-soil-structure system, the damping includes two parts: the material damping and the radiation
damping .The material damping is approximated with the Rayleigh approach. The damping matrix isC=aM+ K (12)
where and are coefficients. The values ofa and are computed by using the first and second modalfrequencies (j=1 andj=2) with equation (13)
)(2
1
2j
j
j
+== (13)
for the steel structure 1 = 2 =1%, and for the reinforced concrete structure 1 = 2 =5%. In this
paper, the equivalent damping ratio [8] is taken as
~
=
+
++ )1(028.0
2036.0
~)~
~1(
~
2
3
3
3
2
2
2
2
hh
ms
s
g
ss
(14)
where ~ is the equivalent damping ratio; and g are the super-structure damping ratio and the material
damping ratio of the soil; s and ~ are the first frequency of the super-structure and the PSSI system; s
is the ratio of the stiffness of the super-structure to the soil, which is computed ass
s
v
hs
*= ; m is the
mass ratio,3
*
a
mm
= ; h is the slenderness ratio,
a
hh
*
= ,and where h*and m* are the equivalent high
and mass of the first mode shape of the super-structure, vs and are shear-wave velocity and the massdensity of the soil,a is the characteristic length of the bottom of the super-structure.The radiation damping which is simulated by the viscous damping elements (COMBIN14) set at the
boundary of the free-field ground can be computed using equation (15) referred to the reference [9].'sc =aimsi (15)
where msi is the mass of the soil layer; ai is valued according to the way proposed by Seed, ai= ii , in
which i =0.05, and i =vsi/(2hsi), his is the thickness of the soil layer.
BUILDING THE MODEL WITH ANSYS
SOFTWARE
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Choosing the element
Using the before-mentioned method, the model is established by ANSYS
software. Seven kinds of
elements are used in this model, which are MASS21, COMBIN14, PLANE42, BEAM3, CONTAC12,
COMBIN40 and LINK1 elements. MASS21 element is used to simulate the mass of the super-structure,
and COMBIN14 element is used to simulate the stiffness of super-structure and the radiation damping at
the boundary of the soil, and PLANE42 element is used to simulate the free-field soil and the raft, and
BEAM3 element is used to simulate the pile, and CONTAC12 element with the contacting ability is usedto simulate the rocking spring of the side of raft, and COMBIN40 element with the contacting and
nonlinear ability is used to simulate the nonlinear lateral soil resistance between the soil and pile. LINK1
element is the dumb element to help simulate floors of the super-structure and the rocking effect.
Building the model
Building the model using ANSYS
software includes two parts: building the geometric model and
building the mechanical model. Building the geometric model uses the direct generation method to define
the nodes and elements of a model directly on the basis of the geometric size. And then, the geometric
model is turned into the mechanical model using constraint equations to establish the special associations
among nodal degrees of freedom and applying the boundary condition to the model. The key problem in
this model is how to simulate the rocking effect of the PSSI system, the actions referred [10] are shown in
Figure 2. First, the cross point of the PLANE42 element simulating the raft, the BEAM element simulating
the pile and the LINK1 element simulating the first floor of the superstructure is turned into rigid point
using the following constraint equation in ANSYS
format.
CE,1,0,2,UY,1,1,UY,-1,3,ROTZ,-b (16)
Then, the LINK1 elements simulating floors are coupled with the cross point using the constraintequations, so that the LINK1 elements simulating floors can keep the same rotation angle with the top of
the BEAM3 element simulating the pile. The constraint equation of the LINK1 element simulating the
first floor is as
CE,2,0,3,UX,1,5,UX,-1,3,ROTZ,- h1 (17)
In the same way, the constraint equations of the LINK1 elements simulating other floors can be generated
in the similar form.
Finally, the two vertical springs to simulate the rocking effect are set at the sides of the raft, with the
constraint equation (18).
Figure 2. Simulating to rocking effect
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CE,4,0,8,UX,1,1,UX,-1 (18)
In this way, the rocking effect can be simulated in the model by ANSYS
software.
ANALYTIC RESULT BY ANSYS
SOFTWARE
In this paper, the transient dynamic analysis (called time-history analysis) is used to analyze the seismic
response of a 4-storey building supported on piles. In ANSYS software, three transient dynamic analysismethods are available: full, reduced and mode superposition, where the full solution method solves
directly and needs no additional assumptions, and is suit to nonlinear problem.
The input motion is the time history of the horizontal displacement and input from the bedrock at the
bottom of the pile group.
Computation model of a 4-storey frame supported on a pile group
A 4-storey and 3-spans frame supported on a pile group with the raft is analyzed as a typical common
structure in II site as shown in Figure 3, and the seismic fortification intensity of the building area is 8.
The weight for the first and the forth floors is 1200kN, the weight for other floors is 1000kN; the first
story stiffness is 0.544105
kN/m, other story stiffness is 0.723105
kN/m; the thickness and width of the
raft are 1m and 4m, the section of the pile is 0.90.9m2, and the length of the pile is 15m, the elastic
modulus of the concrete is 3.0104N/mm
2; the soil around the pile is sand with moderate consistency, the
elastic modulus of the soil: MPa86=E , the Poisson s' ratio of the soil: v=0.25,the angle of internal
friction for soil: = 35 , and 3kN/m15000=hK .
The time history of the horizontal ground acceleration employed is shown in Figure 4, with 3000points at equal spacing of 0.01 sec, and the peak value are 0.22g and 0.40g. This time history of the
acceleration is translated to the time history of the displacement.
Figure.3 4-storey and 3-spans frame supported on
a pile group with the raft
Figure.4 The time history of acceleration from Boston
earthquake (0.22g)The result of analysis
The seismic analysis for the frame using the before-mentioned model is done with the nonlinear pile
foundation under the moderate (the peak of the acceleration is 0.22g) earthquake and large (the peak of
the acceleration is 0.40g). Then this response is compared with the responses of the rigid foundation and
the linear pile foundation to investigate the influence of the pile-soil interaction and nonlinear effect of the
pile foundation on the super-structure.
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The maximum interstory shear, interstory displacement and story displacement of the frame in different
conditions of foundation are computed under the moderate earthquake (0.22g) and the large earthquake
(0.40g). As shown in Table 1 the maximum interstory shear and the minimum story displacement are in
the case of the rigid foundation. The interstory shear of the linear foundation condition is larger than that
of the nonlinear foundation condition, and the story displacement of the linear foundation condition is
smaller than that of the nonlinear foundation condition. The natural frequencies in different conditions of
foundation are shown in Table 2. It can be seen that the natural frequency of the nonlinear foundationcondition is smallest.
The time histories of the displacement of the top story in three different foundation conditions are shown
in Figure 5 for the moderate earthquake (0.22g) and Figure 6 for the large earthquake (0.40g). From
Figures 5 and 6, it can be illustrated that the maximum displacement of the top story is in case of the
nonlinear foundation condition.Table 1. The maximum interstory shear,
interstory displacement and story displacement of the frame
Number of
storymaximum interstory
shear (kN) maximum interstory
displacement )m( maximum story
displacement )m(
Rigid SSI Rigid SSI Rigid SSI
1 1139.0887.0
(1029.0) 0.02090.0163
(0.0186) 0.05000.0559
(0.0570)
2 927.0813.3
(913.1)0.0128
0.0112
(0.0126)0.0542
0.0651
(0.0599)
3 750.8650.6
(728.9)0.0107
0.0093
(0.0104)0.0644
0.0731
(0.0694)
Moderate
earthquake
(0.22g)
4 448.0420.6
(444.8)0.0068
0.0064
(0.0067)0.0711
0.0798
(0.0750)
1 20711996
(19980.0381
0.0367
(0.037)0.0910
0.1060
(0.097)
2 16861716
(1660)0.0233
0.0237
(0.0229)0.0986
0.1244
(0.1219)
3 13651288
(1325)0.0195
0.0184
(0.0189)0.1171
0.1421
(0.1394)
Large
Earthquak
e
(0.40g)
4 814.5789.98
(808.8)0.0123
0.0119
(0.0122)0.1292
0.1585
(0.1449)
annotationThe numerical value in () is the result in the case of the linear foundation condition.
Table 2.Natural frequencies in different foundation conditions
Condition of
foundation
Rigid SSI(linear) SSI(nonlinear)
1 14.85 13.77 6.594
2 18.36 16.89 11.66
3 23.59 21.24 18.64
4 24.51 24.34 24.26The contact states between the pile and the soil is shown in Figure 7 for the moderate earthquake (0.22g)
and Figure 8 for the large earthquake (0.40g). In Figures 7 and 8, "1stat" = stands for that the contact state
between the interfaces of the pile and soil is close, "3stat" = stands for that the contact state between the
interfaces of the pile and soil is open, and "2stat" = stands for that the contact state between the
interfaces of the pile and soil is slip. From Figures 7 and 8, it can be shown that the contact state between
the pile and the soil changes from contact and slippage to separationwith seismic load under the moderate
and large earthquakes.
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(1) Nonlinear foundation condition (1) Nonlinear foundation condition
(2) Linear foundation condition (2) Linear foundation condition
(3) Rigid (3) Rigid
Figure 5. The time history of the displacement of the
top story under moderate earthquake
Figure 6. The time history of the displacement of
the top story under large earthquake
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Figure 7.the contact state between the pile and soil
under moderate earthquake
Figure 8.the contact state between the pile and soil
under large earthquake
CONCLUSIONS
Through the seismic response analysis of the frame supported on a pile group under the moderate andlarge earthquakes, the following conclusions can be summarized:
1. The modified simplified nonlinear pile-soil-structure interaction (PSSI) model can consider the
influence of the free-field on the super-structure directly, the nonlinear effect, and simplified the input
method of Penzien model. Thus, it can be applied to engineering conventionally.
2. The analysis shows that the contact state of the pile and the soil changes from contact and slippage to
separation with the seismic load under the moderate and large earthquakes. So it is necessary to
consider the contact nonlinear effect in PSSI system.
3. In the case of nonlinear foundation condition, the seismic behavior is different from that in the rigid
foundation condition and linear foundation condition.
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5. Technical Code for Building pile foundation. JGJ 94-94. Beijing: China architecture & building
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